The SolverOpts field in the xml-rpc interface only supports the parameters listed in the table at the very end of the Simulation Scripts section of the documentation. The is no provision in the interface to store a system state or change the initialization method.
However, there still could be a means to implement your desired goal.
One approach would be to manually store the system state for different configurations as different models, and then run a series of analyses on those saved cases.
Another alternative (but cumbersome) approach would be to assign all states in your model as variables in your Initialization script. Then, assign each state as an output from your simulation. You could run the model, save the states at the end of the simulation, and then in the script assign the recorded values as the initial conditions for each state on the next simulation run.
I would be interested in hearing any workarounds you have devised as well.